Quantitative Solution of Challenge Problem from Class Activity \#5: You have been hired by Baxter, a company with significant stake in the hemodialysis market (they have exiting products, including the Theranova dialyzer device). Baxter would like to improve the patient experience during hemodialysis by significantly reducing the time required for treatment. They have asked for your help in performing the necessary mathematical modeling to predict the impact of the following dialyzer design changes (individually, not together) on the time required for a single hemodialysis treatment. 1. Increasing the dialysate volumetric flow rate from 500mL/min to 800mL/min. 2. Increasing the number of parallel fibers from 15,000 to 25,000 3. Changing the membrane material to a new poly(amide) that cuts the partition coefficient (blood concentration, relative to dialysate concentration) by 33%. 4. Switching from co-current to counter-current dialysate flow Do not consider combinations of 1-4, as this would significantly complicate the problem. You can make the following simplifying assumptions in this problem: - Only consider urea transport and neglect all other solute (including protein) flow. - The partition coefficient for urea in the blood, relative to dialysate, is normally 1.00 . - The dialyzer base configuration is the same as is listed in the problem statement ( 200m inner fiber diameter, 40m membrane thickness, 20cm length, 300mL/min blood flow, 500mL/min dialysate flow). - You can assume that only a very small volume of blood is in the hemodialyzer at any moment. - An adult patient has about 5L of blood, many orders of magnitude greater than the sum of all hollow fiber lumen volumes. - You can assume that the blood is well mixed and that the inlet and outlet blood urea concentration are constant values until the blood is fully recirculated in the patient (i.e., until 5L are perfused through the hollow fiber device, then the outlet urea concentration becomes the new inlet urea concentration). - The initial blood urea nitrogen concentration at the start of therapy is 150mg/dL (or 1.5g/L ). - You can stop therapy once the blood urea nitrogen concentration reaches the upper end of "normal" (s)